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Context: Theoretical modelling of time-lags between variations in the FeK$\alpha$ emission and the X-ray continuum might shed light on the physics andgeometry of the X-ray emitting region in active galaxies (AGN) and X-raybinaries. We here present the results from a systematic analysis of time-lagsbetween variations in two energy bands ($5-7$ vs $2-4\,\mathrm{keV}$) for sevenX-ray bright and variable AGN.  Aims: We estimate time-lags as accurately as possible and fit them withtheoretical models in the context of the lamp-post geometry. We also constrainthe geometry of the X-ray emitting region in AGN.  Methods: We used all available archival \textit{XMM-Newton} data for thesources in our sample and extracted light curves in the $5-7$ and$2-4\,\mathrm{keV}$ energy bands. We used these light curves and applied athoroughly tested (through extensive numerical simulations) recipe to estimatetime-lags that have minimal bias, approximately follow a Gaussian distribution,and have known errors. Using traditional $\chi^2$ minimisation techniques, wethen fitted the observed time-lags with two different models: aphenomenological model where the time-lags have a power-law dependence onfrequency, and a physical model, using the reverberation time-lags expected inthe lamp-post geometry. The latter were computed assuming a point-like primaryX-ray source above a black hole surrounded by a neutral and prograde accretiondisc with solar iron abundance. We took all relativistic effects into accountfor various X-ray source heights, inclination angles, and black hole spinvalues.

Theoretical modelling of the AGN iron-line vs continuum time-lags in the lamp-post geometry